You posted this in another forum, and said it was a mountain bike. Which is it?
Yes, road bike tires, especially high performance, tacky ones, are thinner than others and thereby more liable to punctures. Tire choice is a series of compromises, weight versus durability, durability versus traction, etc. etc. etc.
You'll need to find the combination that works for your bike, your weight, your riding style, and your roads. If you are so inclined, consider a set of puncture resistant tubes.
Good luck!